CBSE Questions for Class 11 Engineering Maths Straight Lines Quiz 10 - MCQExams.com

Point P(2,3) lines on the $$4x + 3y = 17$$. Then find the co-ordinated of points farthest from the line which are at 5 units distance from the P.
  • $$(6,6)$$
  • $$(6 , -6)$$
  • $$(2 , 0)$$
  • $$(-2 , 0)$$
If a circle $$ { x }^{ 2 }+{ y }^{ 2 }=20$$ meet the parabola $$ { y }^{ 2 }=8x$$ at $$P$$ and $$Q$$. Then $$PQ=$$__ 
  • $$4$$
  • $$8$$
  • $$16$$
  • $$ \sqrt { 5 }$$
The sum of the lengths of tangents and subtangent at a point of $$y=a\log{(x^{2}-a^{2})}$$,$$(a>0)$$ is porportional to
  • $$\left| x\right|$$
  • $$\left| y\right|$$
  • $$\left| xy\right|$$
  • $$\left| x/y\right|$$
Area of the triangle formed by $$(x_{1,}y_{1}),(x_{2},y_{2}), (3y_{2},(-2y_{1}))$$
  • $$ \dfrac{1}{2}\left[ {{x}_{1}}{{y}_{2}}+2{{x}_{1}}{{y}_{1}}-3{{x}_{2}}{{y}_{1}}+3{{y}_{2}}{{y}_{1}}-3{{y}_{2}}^{2} \right] $$
  • $$ \dfrac{1}{2}\left[ {{x}_{1}}{{y}_{2}}+2{{x}_{1}}{{y}_{1}}-3{{x}_{2}}{{y}_{1}}+3{{y}_{2}}{{y}_{1}}-3{{y}_{2}}^{3} \right] $$
  • $$ \dfrac{2}{3}\left[ {{x}_{1}}{{y}_{2}}+2{{x}_{1}}{{y}_{1}}-3{{x}_{2}}{{y}_{1}}+3{{y}_{2}}{{y}_{1}}-3{{y}_{2}}^{2} \right] $$
  • $$ =\dfrac{1}{2}\left[ {{x}_{1}}{{y}_{2}}+2{{x}_{1}}{{y}_{1}}-3{{x}_{2}}{{y}_{1}}+3{{y}_{2}}{{y}_{3}} \right] $$
Find the point on the x-axis which is equidistant from $$(2, -5)$$ and $$(-2, 9)$$.
  • $$(1,2)$$
  • $$(-7,0)$$
  • $$(3,-5)$$
  • $$(8,8)$$
If the points (0,0), $$(3,\sqrt{3})$$ ,(p,q) from an equilateral triangle and $$q_{1},q_{2}$$ are the two values of q then $$q_{1}+q_{2}$$ =
  • $$2\sqrt{3}$$
  • $$\sqrt{3}$$
  • $$-\sqrt{3}$$
  • $$0$$
Three points $$\left( {0,0} \right),\left( {3,\sqrt 3 } \right),\left( {3,\lambda } \right)$$ from an equilateral triangle, then $$\lambda $$ is equal to 
  • $$2$$
  • $$-3$$
  • $$-4$$
  • $$ - \sqrt 3 $$
Find the area of the triangle formed by the mid points of sides of the triangle whose vertices are $$(2, 1)$$, $$(-2, 3)$$, $$(4, -3)$$.
  • $$1.5$$ sq. units
  • $$3$$ sq. units
  • $$6$$ sq. units
  • $$20$$ sq. units
Two points A$$\left ( x_{1},y_{1} \right )andB\left ( x_{2},y_{2} \right )$$ are chosen on the graph of $$f(x)=inx with 0<x_{1}<x_{2}.$$ the point C and D trisect line segment AB with AC<CB. through Ca horizontal line is drawn to cut the curve at$$E\left ( x_{3},y_{3} \right ).if x_{1}=1000$$then the value of$$x_{3}$$ equals
  • 10
  • $$\sqrt{10}$$
  • $$(10)^{2/3}$$
  • $$(10)^{1/3}$$
The points $$(-1,5),(-2,-3),(5,1),(6,9)$$ taken on order are the vertices of a
  • Parallelogram
  • Rhombus
  • Rectangle
  • Suare
The length of a line segment $$AB$$ is $$10$$ units. If the coordinates of one extremity are $$\left(2,-3\right)$$ and the abscissa of the other extremity is $$10$$ then the sum of all possible values of the ordinate of the other extremity is 
  • $$3$$
  • $$-4$$
  • $$12$$
  • $$-6$$
If the line $$\left( \cfrac { x }{ 2 } +\cfrac { y }{ 3 } -1 \right) +\lambda(2x+y-1)=0$$ is parallel to x-axis then $$\lambda=$$
  • $$-\cfrac{1}{2}$$
  • $$\cfrac{1}{2}$$
  • $$-\cfrac{1}{4}$$
  • $$\cfrac{1}{4}$$
The midpoints of the sides of a triangle are $$\left(1,1\right),\left(4,3\right)$$ and $$\left(3,5\right)$$. The area of the triangle is ___ square units.
  • $$14$$
  • $$16$$
  • $$18$$
  • $$20$$
The angle between the lines $$x\cos{30}^{o}+y\sin{30}^{o}=3$$
$$x\cos{60}^{o}+y\sin{60}^{o}=5$$ is
  • $${90}^{o}$$
  • $${30}^{o}$$
  • $${60}^{o}$$
  • None of these
If $$ B (1, 3) $$ is equidistant from $$ A (6,  -1) $$ and $$ C (x, 8) $$, then  $$ x =$$
  • $$3 \text { or } - 5$$
  • $$- 3 \text { or } 5$$
  • $$- 3 \text { or } - 5$$
  • $$3 \text { or } 5$$
If $$x+4y=7$$, where $$y\ \in\ N$$, then the minimum positive value of $$x+y$$ equals
  • $$4$$
  • $$-4$$
  • $$3$$
  • $$1$$
The shortest distance of the point $$(h,k)$$ from both the axes are
  • $$|h|,|k|$$
  • $$(h,k)$$
  • $$\sqrt{h^2+k^2},0$$
  • none of these
Angle between $$x = 2$$ and $$x - 3y = 6$$ is
  • $$\infty $$
  • $${\tan ^{ - 1}}\left( 3 \right)$$
  • $${\tan ^{ - 1}}\left( {\frac{1}{3}} \right)$$
  • None of these
The points$$ (0,1), (-2,3), (6,7), (8,3)$$ form 
  • a parallelogram
  • a rectangle
  • a rhombus
  • a quadrilateral
One vertex of a square $$ABCD$$ is $$A(-1, 1)$$ and the equation of one diagonal $$BD$$ is $$3x+y-8=0$$ then $$C$$=
  • $$(-5, 3)$$
  • $$(5, 3)$$
  • $$(-5, -3)$$
  • $$(2, 5)$$
If the area of triangle formed by the points $$(2a,b),(a+b,2b+a)$$ and $$(2b,2a)$$ be $$\lambda$$ then the area of the triangle whose vertices are $$(a+b,a-b), (3b-a,b+3a)$$ and $$(3a-b,3b-a)$$ will be
  • $$\dfrac{3}{2} \lambda$$
  • $$3\lambda$$
  • $$4\lambda$$
  • $$none\ of\ these$$
If the points ( 5, 1), (1, p) & (4, 2) are collinear then the value of p will be ________.
  • 1
  • 5
  • 2
  • -2
The value of m for which the lines $$3x = y - 8$$ and $$6x + my + 16 = 0$$ coincide is 
  • $$2$$
  • $$-2$$
  • $$\dfrac{1}{2}$$
  • $$-\dfrac{1}{2}$$
If $$\left( \mathbf { a } \cos \theta _ { 1 } , \mathbf { a } \sin \theta _ { 1 } \right) , \left( \mathbf { a } \cos \theta _ { 2 } , \mathbf { a } \sin \theta _ { 2 } \right) \text { and } \left( \mathrm { a } \cos \theta _ { 3 } , \mathbf { a } \sin \theta _ { 3 } \right)$$ represents the vertices of an equilateral triangle inscribed in a circle, then 
  • $$\cos \theta _ { 1 } + \cos \theta _ { 2 } + \cos \theta _ { 3 } = 0$$
  • $$\sin \theta _ { 1 } + \sin \theta _ { 2 } + \sin \theta _ { 3 } = 0$$
  • $$\tan \theta _ { 1 } + \tan \theta _ { 2 } + \tan \theta _ { 3 } = 0$$
  • $$\cot \theta _ { 1 } + \cot \theta _ { 2 } + \cot \theta _ { 3 } = 0$$
A triangle with vertices $$(4,0),(-1,-1),(3,5)$$ is:
  • Isosceles and right angled
  • Isosceles but not right angled
  • right angled but not isosceles
  • Neither right angled nor isosceles
The area of the triangle vertices $$(1,0),(7,0)$$ and $$(4,4)$$ is ___ square units.
  • $$8$$
  • $$10$$
  • $$12$$
  • $$14$$
If the three distance points $$\left( { t }_{ i\quad  }2{ at }_{ i }+{ { at }^{ 3 }_{ i } } \right) \quad for\quad i=1,2,3$$ are collinear then the sum of the abscissae of the points is 
  • -1
  • 0
  • 1
  • 3
Coordinates of trisection of line joining points (-3, -3) and (6, 6) is -
  • (0,0),(3,-3)
  • (0,0),(3,3)
  • (1,1),(3,3)
  • (1,1), (-3,3)
Find the slope of the line $$y = {x^3} - 3x$$ which is parallel to $$2x+18y=9$$.
  • $$2$$
  • $$7$$
  • $$9$$
  • $$-2$$
Number of lines that can be drawn through the point (4, -5) so that its distance from (-2, 3) will be equal to 12 is equal to _________.
  • 0
  • 1
  • 2
  • 3
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